Problem: Simplify the following expression: $r = \dfrac{a}{7} - \dfrac{5a}{9}$
Answer: In order to subtract expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $7$ and $9$ $\lcm(7, 9) = 63$ $ r = \dfrac{9}{9} \cdot \dfrac{a}{7} - \dfrac{7}{7} \cdot \dfrac{5a}{9} $ $r = \dfrac{9a}{63} - \dfrac{35a}{63}$ $r = \dfrac{9a -35a}{63}$ $r = \dfrac{-26a}{63}$